The limitations of MCMC has been addressed with better computational resources and advanced proposal distributions, incorporating gradients [1]}, [2]}. Hamiltonian MCMC sampling methods have been used for Bayesian neural networks [3]} with enhanced computation strategies
[4]}. Langevin MCMC methods have been used in implementation of Bayesian neural networks for pattern classification and time series prediction problems [5]}. A major challenge in MCMC sampling has been in addressing big data and computationally expensive models; hence, surrogate-assisted estimation, in which a low cost surrogate model provides approximation of the likelihood, has been used to address this issue [6]}. Langevin MCMC methods have been used in Bayesian neural networks for transfer learning given multiple sources of data [7]}.
